Measure, Integration & Real Analysis (Hardcover)

Sheldon Axler

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Idioma: inglés

Editorial: Springer Nature Switzerland AG, Cham, 2019

3030331423 / 9783030331429

Serie: Libro 163 de 180 - Graduate Texts in Mathematics

Librería: Grand Eagle Retail, Bensenville, IL, Estados Unidos de AmericaGrand Eagle Retail

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Hardcover. This open access textbook welcomes students into the fundamental theory of measure, integration, and real analysis. Focusing on an accessible approach, Axler lays the foundations for further study by promoting a deep understanding of key results. Content is carefully curated to suit a single course, or two-semester sequence of courses, creating a versatile entry point for graduate studies in all areas of pure and applied mathematics.Motivated by a brief review of Riemann integration and its deficiencies, the text begins by immersing students in the concepts of measure and integration. Lebesgue measure and abstract measures are developed together, with each providing key insight into the main ideas of the other approach. Lebesgue integration links into results such as the Lebesgue Differentiation Theorem. The development of products of abstract measures leads to Lebesgue measure on Rn.Chapters on Banach spaces, Lp spaces, and Hilbert spaces showcase major results such as the HahnBanach Theorem, Hoelders Inequality, and the Riesz Representation Theorem. An in-depth study of linear maps on Hilbert spaces culminates in the Spectral Theorem and Singular Value Decomposition for compact operators, with an optional interlude in real and complex measures. Building on the Hilbert space material, a chapter on Fourier analysis provides an invaluable introduction to Fourier series and the Fourier transform. The final chapter offers a taste of probability.Extensively class tested at multiple universities and written by an award-winning mathematical expositor, Measure, Integration & Real Analysis is an ideal resource for students at the start of their journey into graduate mathematics. A prerequisite of elementary undergraduate real analysis is assumed; students and instructors looking to reinforce these ideas will appreciate the electronic Supplement for Measure, Integration & Real Analysisthat is freely available online. For errata and updates, visit / This open access textbook welcomes students into the fundamental theory of measure, integration, and real analysis. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

N° de ref. del artículo 9783030331429

Título
Measure, Integration & Real Analysis (Hardcover)
Autor
Sheldon Axler
Editorial
Springer Nature Switzerland AG, Cham
Año de publicación
2019
Estado
new
Encuadernación
Hardcover
Idioma
inglés
ISBN 10
3030331423
ISBN 13
9783030331429
Serie
Libro 163 de 180: Graduate Texts in Mathematics

Grand Eagle Retail

Bensenville, IL, Estados Unidos de America

Vendedor de 5 estrellas

Vendedor de AbeBooks desde 12 de octubre de 2005

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